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The fundamental properties of natural numbers
 Journal of Formalized Mathematics
, 1989
"... Summary. Some fundamental properties of addition, multiplication, order relations, exact division, the remainder, divisibility, the least common multiple, the greatest common divisor are presented. A proof of Euclid algorithm is also given. MML Identifier:NAT_1. WWW:http://mizar.org/JFM/Vol1/nat_1.h ..."
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Cited by 685 (73 self)
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Summary. Some fundamental properties of addition, multiplication, order relations, exact division, the remainder, divisibility, the least common multiple, the greatest common divisor are presented. A proof of Euclid algorithm is also given. MML Identifier:NAT_1. WWW:http://mizar.org/JFM/Vol1/nat_1
Fundamental properties of
, 2012
"... This thesis reports a theoretical investigation of the influence of the electronphonon interaction on semiconductor cavity quantum electrodynamical systems, specifically a quantum dot coupled to an optical microcavity. We develop a theoretical description of the decay dynamics of the quantum dot i ..."
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interacting with the cavity and the phonons. It is shown that the presence of the phonon interaction, fundamentally changes the spontaneous emission decay behavior of the quantum dot. Especially in the regime where the quantum dotcavity spectral detuning is significantly larger than any linewidth
M. Eddon Fundamental Properties of Fundamental Properties
"... Two grams mass and three coulombs charge are examples of quantitative properties. Such properties have certain structural features that other sorts of properties lack. How should we account for the distinctive structure of quantity? ..."
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Two grams mass and three coulombs charge are examples of quantitative properties. Such properties have certain structural features that other sorts of properties lack. How should we account for the distinctive structure of quantity?
Voronoi diagrams  a survey of a fundamental geometric data structure
 ACM COMPUTING SURVEYS
, 1991
"... This paper presents a survey of the Voronoi diagram, one of the most fundamental data structures in computational geometry. It demonstrates the importance and usefulness of the Voronoi diagram in a wide variety of fields inside and outside computer science and surveys the history of its development. ..."
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Cited by 743 (5 self)
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This paper presents a survey of the Voronoi diagram, one of the most fundamental data structures in computational geometry. It demonstrates the importance and usefulness of the Voronoi diagram in a wide variety of fields inside and outside computer science and surveys the history of its development
Fundamental properties of Tsallis relative entropy
 J. Math. Phys
"... Abstract. Fundamental properties for the Tsallis relative entropy in both classical and quantum systems are studied. As one of our main results, we give the parametric extension of the trace inequality between the quantum relative entropy and the minus of the trace of the relative operator entropy g ..."
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Cited by 39 (10 self)
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Abstract. Fundamental properties for the Tsallis relative entropy in both classical and quantum systems are studied. As one of our main results, we give the parametric extension of the trace inequality between the quantum relative entropy and the minus of the trace of the relative operator entropy
Fundamental Properties of Aboutness
 IN PROCEEDINGS OF THE TWENTYSECOND ANNUAL INTERNATIONAL ACMSIGIR CONFERENCE ON RESEARCH AND DEVELOPMENT IN INFORMATION RETRIEVAL (SIGIR’99
, 1999
"... Information retrieval (IR) is a reasoning process which is assumed to be driven by determining aboutness (=) between two information carriers (i.e., document and query). Thus, the study of aboutness will be very helpful to set up the theoretical foundations of IR. Aboutness is modeled as a binary ..."
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Cited by 3 (3 self)
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relation over the information carriers (IC). Early studies viewed aboutness as a form of entailment. We regard aboutness as a broader notion. Recent attempts have been made to formalize properties of aboutness which can be expressed as postulates (rules) in terms of information containment, composition
Fundamental properties of harmonic bounding
 In Parallel distributed processing: explorations in the microstructure of cognition
, 2005
"... Evaluation in OT adjudicates competitions between linguistic structures, but it calculates only with the array of violations that the structures incur under each constraint: their violation profiles. Structures with the same profile are indistinguishable, and differences in structure only register t ..."
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Cited by 5 (1 self)
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to the extent that they correlate with differences in violation. General properties that govern relations
Fundamental properties on Tsallis entropies
, 2005
"... Abstract. A chain rule and a subadditivity for the entropy of type β, which is one of the nonextensive (nonadditive) entropies, were derived by Z.Daróczy. In this paper, we study the further relations among Tsallis type entropies which are typical nonextensive entropies. We show some inequalities re ..."
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rules for Tsallis mutual entropies. We give properties of entropic distances in terms of Tsallis entropies. Finally we show parametrically extended results based on information theory. Keywords: Chain rule, subadditivity, strong subadditivity, entropic distance, Fano’s inequality, entropy rate, data
Fundamental Properties of the Galois Correspondence
"... Abstract: Problem Statement: Let K is the splitting field of a polynomial f(x) over a field F and αn be the roots of f in K. Let G be embedded as a subgroup of the symmetric group . We determined the Galois group G, and the subgroup. Approach: computed some auxiliary polynomials that had roots in K, ..."
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Abstract: Problem Statement: Let K is the splitting field of a polynomial f(x) over a field F and αn be the roots of f in K. Let G be embedded as a subgroup of the symmetric group . We determined the Galois group G, and the subgroup. Approach: computed some auxiliary polynomials that had roots in K, where the permutation of a set was considered distinct. The Galois Theory was deduced using the primitive element and Splitting theorems. Results: The Galois extension K/L to identity L and its Galois group is a subgroup of G. which was referred to as the main theorem which we proved. Conclusion: Hence the findings suggest the need for computing more auxiliary polynomials that have roots.
Results 1  10
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994,317